Statistics of vertical backscatter profile of cirrus clouds

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11, 25813–25870, 2011

Cirrus backscatter profiles statistics

P. Veglio and T. Maestri

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Atmos. Chem. Phys. Discuss., 11, 25813–25870, 2011 www.atmos-chem-phys-discuss.net/11/25813/2011/ doi:10.5194/acpd-11-25813-2011

Atmospheric Chemistry and Physics Discussions

This discussion paper is/has been under review for the journal Atmospheric Chemistry and Physics (ACP). Please refer to the corresponding final paper in ACP if available.

Statistics of vertical backscatter profile

of cirrus clouds

P. Veglio and T. Maestri

Physics Department, Alma Mater Studiorum, University of Bologna, Bologna, Italy

Received: 23 July 2011 – Accepted: 6 September 2011 – Published: 16 September 2011

Correspondence to: P. Veglio (paolo.veglio3@unibo.it)

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Abstract

A nearly global statistical analysis of vertical backscatter and extinction profiles of cirrus clouds collected by the CALIOP lidar, on-board of the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation, is presented.

Statistics on frequency of occurrence and distributions of bulk properties of cirrus

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clouds in general and, for the first time, of horizontally homogeneous (on a 5-km field of view) cirrus clouds only are provided. Annual and seasonal backscatter profiles (BSP) are computed for the horizontally homogeneous cirri. Differences found in the day/night cases and for midlatitudes and tropics are studied in terms of the mean phys-ical parameters of the clouds from which they are derived.

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The relation between cloud physical parameters (optical depth, geometrical thick-ness and temperature) and the shape of the BSP is investigated. It is found that cloud geometrical thickness is the main parameter affecting the shape of the mean CALIOP BSP. Specifically, cirrus clouds with small geometrical thicknesses show a maximum in mean BSP curve placed near cloud top. As the cloud geometrical thickness increases

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the BSP maximum shifts towards cloud base. Cloud optical depth and temperature have smaller e_ffect on the shape of the CALIOP BSPs. In general a slight increase in the BSP maximum is observed as cloud temperature and optical depth increase.

In order to fit mean BSPs, as functions of geometrical thickness and position within the cloud layer, polynomial functions are provided. The impact on satellite radiative

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1 Introduction and motivations

The persistence of high-level clouds, that normally cover more than 20 % of the globe (Wylie et al., 1994), suggests that they play an important role in the Earth energy bud-get. At midlatitudes (ML) they exhibit an almost constant coverage and their presence is about 40 %. At these latitudes ice clouds are generated both by large-scale ascent

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and atmospheric waves activity (Lynch, 2002). In the tropics, a maximum of occur-rence has been observed near the equator (∼70 %) and a minimum one (<10 %) in the subtropical regions (Wylie et al., 2005). Deep convection is the engine that produces tropical ice clouds. In particular, thin cirrus clouds in the tropics are mainly formed by iced particles flowing out from the convective core of cumuli at cloud top.

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The radiative impact of ice clouds is crucial to determine the energy balance of the Earth atmosphere since their albedo and greenhouse effects are of the same order of magnitude (McFarquhar et al., 2000). In the upper troposphere, the energy balance in presence of ice clouds depends on several cloud parameters such as cloud top height and thickness, Ice-Water-Content (IWC), optical depth (OD) and ice particle

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size distribution (PSD) (Liou, 1986; Maestri and Rizzi, 2003).

The different cirrus cloud formation processes occurring at ML and tropics influence the distribution of mass, particle sizes and ice crystals habits within the clouds and possibly affect their radiative properties. Unfortunately, due to the very extreme con-ditions, in situ measurements of high clouds microphysical properties are technically

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difficult (McFarquhar and Heymsfield, 1996). In particular, field campaigns focused on the vertical characterization of ice clouds properties are few if compared to the large variability and occurrence of this type of clouds (Wendisch et al., 2005), and, thus, current databases do not appropriately reproduce the possible heterogeneity found in nature.

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how the assumption on the vertical distribution of IWC might impact cloud properties retrievals (OD and particle effective dimension) from infrared satellite measurements. Chiriaco et al. (2006), while highlighting the potentialities of using combined visible (532 nm) and infrared (10.6 µm) lidar observations for retrieving vertically resolved pro-files of particle absorption efficiency, particle concentration and IWC, show the

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tance of determining the position of the maximum of absorption within a cloud layer and provide an example of the large variations in the retrievals of the particles effective sizes for different hypotheses on where maximum of absorption takes place. Along the same line of research, Zhang et al. (2010) demonstrate that homogeneous cloud assumption (of ice particle size) on the vertical can affect the solar reflected bi-spectral

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and infrared split-window methods to di_fferent extents and, consequently, can lead to significantly different retrievals of effective dimensions and IWC.

The present work deals with thin cirrus clouds which, among ice clouds, are partic-ularly di_fficult to characterize due to their altitude and low IWC. It aims at (i) improving the knowledge and characterization of vertical properties of cirri, (ii) contributing to the

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refinement of the interpretation of remote sensing data and (iii) decreasing the uncer-tainties related to the computations of radiative fields (which, currently, are normally generated assuming homogeneity in the cloud features along the vertical). At this pur-pose, the vertical backscatter and extinction coefficient profiles within cirrus clouds are investigated. The work is based on active remote sensing data since the investigation

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of vertical cloud properties using passive remote-sensing measurements is subjected to some limitations. Passive sensors are mainly used to retrieve cloud top height, wa-ter phase and bulk optical or microphysical properties (King et al., 2004; Baum et al., 2005a,b). Only recently, a tentative analysis was done by Wang et al. (2009) who developed an algorithm to derive ice particles effective sizes of cloud top and bottom

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On the other hand, active sensors such as lidars and radars, under certain circum-stances, allow a better description of specific vertical properties of cloud layers. Lidar systems are very suitable to observe vertical characteristics of thin ice clouds, while radars mostly miss the detection of cloud layers with small ice crystals, like those found in high-level cirrus clouds that are the subject of the present study.

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Current lidars can sense scattering layers with visible OD lower than about 3. Un-til few years ago, these instruments were mostly ground-based and thus only scat-tering layers at the zenith of the measuring site could be observed. When high clouds are studied using lidar observations, the up-looking measurement configura-tion shows some disadvantages: both low-level clouds and thick aerosol layers

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tenuate the lidar pulse, often preventing the possibility to sense high tropospheric clouds. For this reason data from the Cloud-Aerosol LIdar with Orthogonal Polar-ization (CALIOP), on-board the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) launched on orbit in 2006 by NASA, are used. CALIOP pro-vides continuous global observations of the atmosphere and a new vision of the upper

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troposphere with focus on thin, high clouds.

CALIOP global observations have been extensively utilized to perform statistical analysis of some cirrus clouds physical parameters. For example, Berthier et al. (2008) used CALIOP lidar, in combination with LITE (Lidar In-space Technology Experiment) and GLAS (Geoscience Laser Altimeter System), to assess the vertical distribution of

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cloud altitudes on a global extent. Holz et al. (2008) performed a study of the cloud top height comparing the measurements obtained from CALIOP with the ones retrieved from MODIS. Nazaryan et al. (2008) used CALIOP data to investigate the occurrence frequency of cirrus clouds on a near-global scale as a function of time, latitude, and altitude. Cho et al. (2008) combined a year of CALIOP and MODIS data to study

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sensors together. They provide a measure of the cirrus clouds occurrence depending on latitude, height, surface type and season for a year of data. Martins et al. (2011) made use of 2.5 years of CALIOP nighttime data in order to investigate properties of cirrus clouds such as thickness, top altitude and midlayer temperature, and put them in relation to atmospheric dynamics and water vapor. As many others, the above cited

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works show that one of the advantages offered by CALIOP, with respect to ground-based lidars, is its global and down-looking view of the atmosphere.

The present work, which is focused on CALIOP data in presence of ice clouds in the upper troposphere, provides the first analysis, on a nearly global scale, of the vertical structure of the extinction and backscatter coefficients of cirri and investigates

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the vertical profile of high, optically thin clouds. Only cirrus clouds with nearly constant top and base altitude in a 5-km field of view are selected for the analysis so that possible artifacts due to geometrical inhomogeneities are removed. Statistics concerning the frequency of occurrence and the cloud physical features of horizontally homogeneous cirrus clouds are provided, for the first time, and compared to those obtained for cirri in

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general. The vertical extinction profile (ETP) and the vertical backscatter profile (BSP) are strictly related to the vertical distribution of the IWC which, in turn, is fundamental to determine the radiative effect and the energy balance of the cloud layer and is a prognostic variable inside Numerical Weather Prediction (NWP) and Climate Models (CM). The main goal of this study is to analyze the statistical features of cirrus clouds

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vertical extinction and backscatter profiles collected at midlatitudes and tropics over the ocean. A statistic of the shape of the CALIOP BSPs (and ETPs) of cirrus clouds is thus derived. The dependence of the profiles on physical parameters, such as cloud optical depth, cloud geometrical thickness (∆z) and temperature, is also investigated and a classification of ice clouds based on the vertical features of the BSPs (and ETPs) is

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provided.

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for iced, optically thin clouds in general. In Sect. 3 annual and seasonal BSPs are computed for night and day and for tropics and midlatitudes. The influence of the main atmospheric and cloud parameters on mean BSPs is studied. Fitting functions, that describe the mean shape of the BSP as function of the cloud geometrical thickness, are derived. Section 4 dwells on the relation of the BSP with ice content profile. The

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analytical fitting functions, describing the climatological shape of the BSPs, are used as inputs in a forward radiative transfer model to evaluate the impact of the CALIOP-derived IWC profiles with respect to assuming a constant IWC profile. A summary is given in Sect. 5.

2 Data set and methodology

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Data analyzed in this study cover the full year 2008, so that all the meteorological seasons can be investigated. Two distinct CALIOP products (http://www-calipso.larc. nasa.gov/resources/calipso users guide/data summaries/) at 5-km horizontal resolu-tion, version 3, are used: 1) the Level 2 cloud layer (CLay) and 2) the Level 2 cloud profile (CPro) files (Anselmo et al., 2007).

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The CLay content has column and layer descriptors. The column descriptors con-tain information on temporal and geophysical location and details on surface type, sunlight conditions and number of cloud layers. Each layer is then described by the layer descriptors, which provide information on spatial and physical characteristics of the scattering layers. The CLay parameters here used are: cloud top and base

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altitude (z_t and z_b), cloud optical depth (τ), latitude and longitude of the instanta-neous field of view (iFOV), UTC time of measurement, layer midpoint temperature and the feature classification flags (see http://www-calipso.larc.nasa.gov/resources/ calipso users guide/data summaries/layer/#feature classification flags). The midlayer temperatures contained in the CLay data are derived from the GEOS-5 (Goddard Earth

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The CPro files provide information on the whole atmospheric column and, in par-ticular, contain the measured vertical profiles of particulate backscatter and extinc-tion coefficients. The backscatter coefficient (β′(z), including particulate and molecular components) is derived from the measured attenuated backscatter:

β_a(z)=β′(z)T2(z) (1)

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whereT2is the two-way transmittance. The derivation of the particulate backscatter coefficient (β(z)) from the above equation requires estimation of additional quantities (i.e. multiple scattering factor) and ancillary data (i.e. molecular number density and ozone absorption coefficient profiles) whose calculation might lead to errors and un-certainties in the retrieved products, as discussed in http://www-calipso.larc.nasa.gov/

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resources/pdfs/PC-SCI-202 Part4 v1.0.pdf. In the present study it is assumed that any measurement uncertainty and error associated with cloud products retrieval do not systematically affect the shape of the BSP (and ETP).

The uncertainties associated with the particulate backscatter and extinction coef-ficients in the Level 2 data bring to estimate percentage errors of the order of 40–

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50 % along the cloud body, both for backscatter and extinction coefficient. The per-centage errors are usually larger (of a factor 2 or even 3) close to cloud base and top where the backscatter signal might be very low. All the errors are considered random and totally uncorrelated (http://eosweb.larc.nasa.gov/PRODOCS/calipso/pdf/ CALIOP Version3 Extinction Error Analysis.pdf).

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Once the particulate backscatter is retrieved, the particulate extinction (σ(z)) at level

zis obtained by multiplying by the appropriate particulate lidar ratioS_P:

σ(z)=S_Pβ(z). (2)

Note that in the CALIOP data processing, to derive analytical solutions from the lidar equation, the lidar ratio is constant throughout a feature layer (i.e. a cloud). As a

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BSPs. The backscatter coefficient profile is derived from the 532 nm laser data. Its vertical resolution is 60 m (from ground level up to a height of 20.2 km). Horizontal resolution of CPro (and corresponding CLay) data is 5 km, obtained by measures of 15 iFOVs of about 80 m each.

2.1 Cirrus clouds selection: Reduced Database

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The present study is focused on tropical and midlatitude areas. Three latitudinal belts are initially defined: tropics (30◦S–30◦N), midlatitudes North (30◦N–60◦N) and mid-latitudes South (30◦S–60◦S). The distinction is done considering the different phys-ical processes that characterize these regions, such as stronger convection in tropi-cal zones, different mean circulation, diverse cloud formation processes (Lynch, 2002;

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Holton, 2004; Sassen et al., 2008). Data collected in polar regions (above 60◦N and be-low 60◦S) are excluded from the database since the quasi-polar orbit of the CALIPSO satellite causes oversampling of very high latitude areas.

A reduced database (RD), consisting of data concerning high-level iced clouds only, is derived from the full database containing all the CLay and CPro files of year 2008

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(about 20000 files for a total of around 80 millions FOVs). CALIPSO ETPs and BSPs are selected and stored into the RD if all the conditions listed in Table 1 are met. These conditions are applied to ancillary data of the CLay files to obtain a RD consisting of BSPs (and thus ETPs) of high-altitude, optically thin ice clouds over the ocean.

Cloud base threshold altitude is set at 5 km at both ML and at 8 km at tropics (TRO)

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similarly to what done in previous works (Nazaryan et al., 2008; Eguchi et al., 2007). Clouds with optical depth larger than 10−3 and less than 2 only are selected. As in Martins et al. (2011) cloud layers with optical depth smaller than 10−3 are removed because they are considered to be below the threshold confidence of lidar data and can be attributed to noise. Maximum optical depth allowed is set at 2.0 so that the full

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The selection of ice phase clouds only is obtained through the use of multiple require-ments: altitude of base and top (conditions 2 and 3 of Table 1), midpoint temperature (i.e. the temperature at the geometrical middle-point of the cloud thickness, condition 4) and above all the use of CALIOP Feature Classification Flags (condition 5). As in Nazaryan et al. (2008) only those cloud layers from the CALIPSO data record that are

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identified by the CALIOP cloud-aerosol discrimination (CAD) algorithm as clouds with high level of confidence (Feature Type QA equals 3) are selected. To avoid the pres-ence of supercooled water clouds in our reduced database further conditions provided by CAD algorithm and concerning the cloud phase are used: the Ice/Water Phase field of the Feature Classification Flags must be either randomly or horizontally oriented ice

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particles.

Requirement number 6 in Table 1 (“Cloud Layer” equals “upper-layer” cloud) is in-troduced to account for multiple-layer clouds. When more than one scattering layer in the same FOV is detected, only the first one (i.e. the highest) is considered, and its backscatter (extinction) profile is recorded into the RD. This criterion allows the

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clusion of the BSP of the upper layer of condensate into the RD when conditions of multiple-layer clouds are found.

When all the conditions listed in Table 1 are met, the BSPs contained in the CPro file are copied in the RD. Each selected profile is recorded together with the corresponding ancillary data taken from the CLay. Repetition of the same procedure for all the FOVs

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contained in the CPro files of year 2008 completes the RD. The clouds contained in the RD are simply referenced as cirrus clouds or cirri in what follows.

Some basic statistic concerning the frequency of occurrence of cirrus clouds se-lected for the RD is given in Table 2. The table shows that, on average, cirrus clouds cover more that 30 % of ocean FOVs from 60◦S to 60◦N with a maximum in the

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differences in the selection criteria, the absolute values of the cirrus clouds frequency do not exactly match what found by previous authors; nevertheless the general fea-tures of the statistical ensemble are preserved, i.e., cirrus clouds during nighttime have higher occurrences in tropical areas and lower occurrences in the midlatitude belts with respect to what found during daytime in the same areas, as in Nazaryan et al. (2008).

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The main physical and optical characteristics of the cirrus clouds selected for the RD are described by means of percentage distributions in Fig. 1 for tropics and midlatitudes and for nighttime and daytime separately. It is shown that at tropics the mean top altitude is 14.5 km during the day and 14.8 km during the night while at ML it is about 10.2 km and 10.4 km respectively for day and night. These values are in very good

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agreement with what found by Nazaryan et al. (2008) and Martins et al. (2011). The geometrical thickness distributions are highly peaked at 0.8 km at day and at around 1 km at night for both latitudes denoting the widespread occurrence of thin cirri. The mean thickness is larger during the night than at daytime with very similar values for both latitudes (about 2.1 km at night versus 1.6 km during the day). The thickness

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distribution at tropics is in accordance with Martins et al. (2011) while at ML some differences are found, possibly due to the very stringent condition applied on cloud midlayer temperature (maximum at 233 K) by the cited authors. The OD distributions show the high predominance of optically thin cirrus clouds (especially during nighttime) and a monotonic and rapid percentage decrease from 10−3 to 2 optical depth. The

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lower-right panel of Fig. 1 shows the distributions of the midpoint cloud temperature. For the midlatitude case both day and night midlayer temperature distributions are almost equally spread around the mean value (226 K) while for the tropical case the distributions for night and day data show (again very similar and with a mean value of around 209 K) a higher degree of asymmetry and a longer tail toward the larger

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2.2 Definition of the final database

Backscatter (and extinction) profiles contained in the RD refer to cirrus clouds covering a wide range of vertical extents (from few hundreds m up to 8 km) and optical depths (from 10−3to 2).

The cloud geometrical thickness is proportional to the integer number of the

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backscatter (or extinction) coefficient values used to describe the layer in the CPro files that have a vertical resolution of 60 m. On the other hand, the total layer optical depth influences the magnitude of the layer-backscattered signal. Since we are interested in deriving statistical features of the shape of the BSPs (and ETPs) and investigating if relations with some of the main atmospheric parameters (included cloud’s OD and∆z)

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exist, data are subjected to a process of rescaling and normalization. Thus a compar-ison among the shape of profiles, which originally would differ for the total amount of energy backscattered to the sensor and for the number of scattering levels, is made possible.

Moreover, a procedure that discards all the FOVs with non-uniform cirrus clouds

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geometrical features is also applied. The operation is performed to avoid that possible horizontal variations in cloud top and base altitude, within the 5-km resolution CALIOP data, might affect the averaging process of the shape of the BSPs.

These operations, described in detail in the two following subsections, lead to the creation of a new database called the Final Database (FD) over which the analysis of

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the BSPs (and ETPs) is performed.

2.2.1 Homogenization

With the term homogenization the operation of selecting cirrus clouds with horizontally homogeneous top and base altitudes is meant.

The 5-km horizontal resolution Level 2 data products (CLay and CPro)

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pdf, http://www-calipso.larc.nasa.gov/resources/pdfs/PC-SCI-202 Part2 rev1x01.pdf) to averaged Level 1, full resolution, attenuated backscatter profiles, in order to obtain high signal-to-noise ratios (SNR). Since horizontal inhomogeneities could introduce artifacts in the analysis of the shape of the BSPs, the non-uniform 5-km horizontal resolution FOVs are discarded from the database.

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The criterion used to define the geometrical horizontal homogeneity within the 5-km horizontal resolution CALIOP FOVs is based on the analysis of cloud top and base height retrieval at higher resolution (i.e. 1 km). Cloud top and base altitudes stored in the Level 2 CLay at 1-km horizontal resolution are collocated with the same products of the 5-km CLay files selected in the RD. For each 5-km FOV, the cloud top and

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base heights (z_t and z_b) are respectively compared to the mean cloud top and base heights (z_t_{1 km}andz_b_{1 km}) obtained by averaging the five cloud top and base products of corresponding 1-km CLay files. The results are finally divided by the cloud thickness, as shown in the following equations:

Zt₌|zt−zt1 km|

∆z (3)

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Zb₌|zb−zb1 km|

∆z (4)

It is assumed that a horizontally uniform cirrus cloud fills the observed 5-km FOV when-ever both the conditionsZt <0.1 andZb <0.25 are met. The condition on the cloud top homogeneity is more stringent than the one on cloud base since its derivation is performed on data with higher SNRs.

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2.2.2 Rescaling and normalization of Extinction and Backscatter Profiles

The rescaling process is obtained by using a linear interpolation. The original BSPs (and ETPs) are rescaled to a standard length of 60 points (I height indexes). This means that, regardless of the geometrical thickness of the cloud, the rescaled BSPs (ETPs) are described by 60 values of the backscatter (extinction) coefficient. The

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height indexes are equally spaced.

The backscatter coe_fficient at height indexh,β(h), assumes di_fferent values which are strongly correlated with the cloud-layer optical depth. A normalized backscatter coefficient,β_n(h), is obtained by dividing the level-backscatter profile by the total area of backscatter profile (computed from cloud-base to cloud-top altitude). Since this

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operation is performed after the height rescaling at I₌60 equally spaced points, the total area is obtained by a simple summation. Using the trapezoidal rule the normalized backscatter coefficient at level (height index)his written as:

β_n(h)= _β₍₁₎₊_β₍_I₎β(h)

2 +

PI−1

h=2β(h)

(5)

At this stage, normalized backscatter profiles from cirrus clouds with different ODs are

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comparable and stored in the final data set. In Fig. 2 an example of the normalization and rescaling process, for two randomly selected BSPs, is shown.

Along with the normalization procedure an additional data filtering process is applied to the database. The process is based on the analysis ofβ_n(h). This quantity should be positive for all the 60 height indexesh, unless for data having a SNR smaller than 1

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or for bad instrument calibration.

In this regard, BSP data derived from CPro files and selected in the RD may show two kinds of problems: (1) profiles with some negative backscatter values and (2) pro-files with some zero backscatter values between the cloud-top and cloud-base height. If one of the two cases occurs the profile is discarded from the final data set.

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2.2.3 Statistical features of the Final Database

The analysis of the shape of BSP is performed on the ensemble ofβ_n(h) contained in the FD. The subscript n is omitted in the following, and for sake of simplicity, this quantity is called BSP. Since the shape of BSPs and ETPs is the same, only results concerning BSPs are shown. Cloud geometrical depths, BSPs (and ETPs) total areas

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(see Eq. 5) and all the other ancillary data are recorded in the final database, so that the original BSPs (and ETPs) might be reconstructed at any time.

The FD consists of about 1.5 million cirrus cloud cases: about 43 % of the total is found in the tropics and the remaining at ML (37 % in the ML South and 20 % in the ML North). In Table 3 the percentage of CALIOP FOVs selected for the FD, with respect

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to the total number of FOVs observed over the sea at the same latitudinal areas in 2008, is reported. Table 3 gives an idea of the occurrence frequency of horizontally homogeneous cirrus clouds over the ocean which are detected in approximately 8 % of the 5-km horizontal resolution CALIOP FOVs. Statistics for daylight and nighttime occurrence are also considered. With respect to those reported in Table 2 and referring

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to the RD (that concerns cirrus clouds in general), the occurrence frequencies reported in Table 3 are drastically reduced. In particular, high percentages of optically (and geometrically) thin cirrus clouds present in the RD are excluded from the FD.

This is also shown in Fig. 3, which highlights the general physical and optical fea-tures of the geometrically homogeneous cirrus clouds contained in the FD for tropics

20

and ML and for day and nighttime separately. The frequency distributions of cloud top height (upper left panel) are very similar to those shown in Fig. 1. Only slight shifts toward higher altitudes at ML and toward lower altitudes at tropics for the FD are ob-served. The largest changes, with respect to what shown for the RD, are found in the geometrical thickness and optical depth distributions. The occurrence frequencies

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around a 50 % increase with respect to what found considering all cirrus clouds. The ODs frequency distributions are also drastically changed and mean ODs are shifted to higher values (about 0.96 for ML and 0.83 for tropics). Some changes are also found in the midlayer temperature, which is increased (about 1 K for the ML and 6 K for the tropics) with respect to what found for the RD.

5

In Table 4 some statistics concerning the occurrence of overlapped clouds are given for day and night. The table shows that, at midlatitudes, more than 50 % of the FOVs that are selected in the FD consists of non-overlapped clouds. The number increases at tropics and involves about two-thirds of clouds of the FD when day and night cases are considered together. Note that for the RD the percentage of overlapped cirrus

10

clouds is significantly higher (not shown here).

3 Analysis of CALIOP vertical Backscatter and Extinction Profiles

A detailed statistical analysis of the shape of the BSPs is performed accounting for the whole FD (horizontally homogeneous cirrus clouds). The influence of cloud physical parameters (mainly geographical location, cloud optical depth, geometrical thickness

15

and temperature) on cloud vertical features of the BSP is investigated. This requires the definition of a mean vertical BSP and, for each height index, a mean value of the backscatter coefficient is derived. Since the processes of averaging are performed on the full FD, which includes clouds with very different physical and geometrical proper-ties, the problem of the shape of the distribution of data around the mean (for each

20

altitude level) arises. For the present study, at each altitude level (height index), the definition of a mean backscatter (BS) value makes sense only if the data are approxi-mately symmetrically distributed around a maximum value.

All the means obtained in this work are such that the distribution of the backscatter values at each height index is unimodal and approximately symmetric. As a

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3.1 Definition of the Difference Index

To evaluate the results of the analysis, an index quantifying the distinction between two (mean) BSPs is also needed. A Difference Index,I_∆, is then defined as:

I_∆=

PI

h=1|β(h)−β

∗ (h)|

β(1)+β(I)

2 +

PI−1

h=2β(h)

·100 (6)

whereβ(h) is a reference BSP andβ∗(h) is the BSP that has to be evaluated against

5

the reference one. I is again the total number of points along the cloud height (60). The difference index is preferred to other indexes (such as the squared differences) because of its simple interpretation. In fact, it represents the percentage value derived from the ratio of the area between the two BS profiles and the total area of the mean reference BSP. Equation (6) can be simplified noting that the denominator (that is the

10

area of the reference BSP) is equal to unity, as a consequence of the normalization of all the profiles contained in the final database.

3.2 Annual and seasonal averages of the backscatter profiles

Due to appreciable differences found in the mean physical characteristics of cirrus clouds measured during night and daylight hours (Fig. 3), BSPs collected at nighttime

15

and daytime are analyzed separately. Measurements obtained at midlatitudes and tropics are studied individually too.

Annual means of the shape of the BSPs are given as functions of the 60 height indexes: height index number 1 is cloud base and number 60 is cloud top. Results are plotted in Fig. 4 and show smooth curves with a single maximum BS value located

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close to cloud midlayer. Very similar profiles for tropics and ML, both at daylight and at nighttime, are observed, thus showing a minor influence of latitude on annual mean BSPs. Note that the distributions of geometrical thickness for homogeneous cirrus clouds at ML and at tropics are very similar while some differences are observed in the cloud top height, optical depth and temperature distributions (see back at Fig. 3).

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In contrast, the differences between mean BSPs measured during the night (dashed curves in Fig. 4) and during the day (solid lines) are significant. A broader mean BSP shape in case of daylight cirri is observed with respect to nighttime. In terms of I_∆

the differences are of the order of 10 % for both latitudes. Physical characteristics reported in Fig. 3 showed that the main differences between night and day distributions

5

are found in the cloud geometrical thickness, suggesting a possible influence of this parameter on the shape of the CALIOP BSP.

From Fig. 4 it is also observed that the mean value of the normalized BS coefficient measured at cloud base during night is lower than that measured during daylight hours. This result can be interpreted either as a CALIOP higher ability to detect cloud base

10

during the night than day due to higher SNRs or as a physical signal that would mean that, on average, sharper cloud base edges are found during the day.

The averaging process is also applied to monthly data, around 25 000 cirrus clouds profiles per month. Results (not plotted here) show very little variability on the shape of the BSP with the period of the year. The maximumI_∆ value found when monthly

15

mean BSPs are compared to the corresponding annual means is less than 5.5 % at ML (North and South ML are studied separately in this regard to highlight the seasonal signal) and less than 2.7 % at tropics (for both North and South tropical belts).

Despite the small difference index, the two main climatic regions (ML and tropics) are studied separately in the next subsections that are focused on the investigation of

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possible relations among the shape of the BSP and cloud physical and thermodynamic parameters. Due to the minimal seasonal variability observed in monthly mean BSPs, all data presented in what follows are averaged on a full year period.

3.3 Geometrical thickness and Backscatter Profile

In order to investigate the influence of the cloud geometrical thickness on the shape

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of the intervals is chosen so that at least 2000 profiles are selected for each subset. In Appendix A a methodology that derives the minimum number of profiles per subset, which is required to have a statistically relevant ensemble (for subsets of the whole FD), is described.

Results for midlatitudes and tropics are shown in Figs. 5 and 6 for nighttime and

5

daytime respectively. It is observed that, for all the cases presented in the figures, the maximum of the BS profile is close to cloud top for thin cirrus clouds and moves towards cloud base as the cloud geometrical depth increases. For each panel of the figures, the difference indexes, which evaluate the diversity of each curve with respect to the mean BSPs (for midlatitudes and tropics and for night and day, as already shown in

10

Fig. 4), are computed. Results show a great variability among the mean BSPs:I_∆is at maximum of about 38 % for midlatitudes and tropics during the night and 36 % during the day. The variability among mean BSPs of cirrus clouds of selected geometrical thickness intervals suggests a strong relation between cloud depth and the shape of the BSP.

15

The mean backscatter profiles plotted in Fig. 5 and 6 are analyzed as distributions along the height-index axis and their skewnesses are calculated. Results show that negative skewness values are found in case of night clouds with∆zless than 3 km both at tropics and ML, while positive ones are observed if the∆z is larger than 3 km. For the daylight case the geometrical vertical extent defining the ensembles with negative

20

or positive skewness is 2 km both for midlatitude and tropical cirrus clouds. Note that a negative skewness value means a BS maximum placed in the upper part of the cloud while a positive one indicates a BS maximum in the lower part of the cloud.

Differences between BSPs of midlatitude and tropical data for cirrus clouds belong-ing to the same interval of geometrical thickness are minor but appreciable (difference

25

indexes are about 6.5 % for daylight and 8.5 % for nighttime data respectively). Diff er-ences of the same order of magnitude are found also when tighter intervals of geomet-rical thickness are considered (i.e. intervals of width of 0.5 km or less). Very narrow

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within each interval might influence the results of the comparison among data collected at the two latitudes. The discrepancies found between midlatitude and tropical mean BSPs cannot, thus, be explained in terms of cloud geometrical thickness only and it implies that other parameters, characterizing differently midlatitude and tropical cirrus clouds, might influence the shape of the CALIOP BSP.

5

In our analysis only cloud bulk parameters, such as optical depth and temperature, are investigated while vertical variation of microphysical features (i.e., PSD or particles habit type) are not considered since no information is available for the cases analyzed in the present study. In this regard, note that, due to the environmental difficulties of collecting these kind of data, only rare and sparse measurements are accessible.

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Comparison between in situ data collected for tropical and midlatitude cirri show that PSDs measured in ice clouds associated with deep convection exhibit an exponen-tial size distribution behavior, while, typically, midlatitude cirri display narrower PSDs (Heymsfield and Miloshevich, 2003; Baum et al., 2005a,b; Sassen et al., 2008). Nev-ertheless, it is the vertical variation of the PSD or of the particles’ habit that might

15

influence the shape of the BSP; unfortunately, in this regard, available data are few, for certain aspects in contrast among them and not easily interpretable in this context (Heymsfield and Miloshevich, 1995; Lawson et al., 2006). It is worth noting again that, in the CALIOP data processing, the lidar ratio is constant throughout a feature layer, meaning that variations of the PSD or the habit type are not accounted for.

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Nighttime and daytime data show large discrepancies even when cirrus clouds within the same thickness interval are compared (dashed curves plotted in the panels of Fig. 5 with the corresponding solid lines plotted in Fig. 6). In this case theI_∆ is of the order of 20 % for both latitudes. This again suggests that possibly different physical features characterizing the two cases might influence the shape of the BSP. The influence of

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3.4 Optical depth and backscatter profile

Similarly to what was done for investigating the relation between cloud BSP shape and geometrical thickness, an analysis concerning the cirrus optical depth and the backscatter profiles shape is performed. The final database is divided into multiple sub-sets containing cirrus clouds with differentτ. For each subset a mean BSP is computed

5

at tropics and midlatitudes and for data collected during the night and day separately. Results (not shown here) are very similar to what obtained previously in the analysis concerning the geometrical thickness and BSPs relation. In fact, the maximum in the shape of the mean BS curve is close to the cloud top for clouds with very smallτand to the base for the optically thickest clouds of the ensemble (FD). In terms of skewness

10

the BSP mean curves show negative values for OD values less than approximately 1.3 at night and 0.8 at day. Nevertheless, in the present analysis, the dependence between the cloud BSP shape and its optical depth is of minor intensity with respect to the one found for the geometrical thickness. In fact,I_∆computed for the mean BSP of each OD interval and the corresponding annual average is at maximum of 22 % (it was almost

15

40 % in the analysis concerning_∆z). Furthermore, some exceptions are found to the rule describing the general behavior (BSP maximum moves toward cloud base as τ

increases).

A correlation exists between cloud geometrical thickness and optical depth. An ex-ample of this is shown in Fig. 7 where cloud optical depth is plotted as function of

20

cloud geometrical thickness for data collected in the tropical and midlatitude regions and during the day or at night (the four red and blue lines in the plot). The curves show a monotonic increase of the averaged OD value for any increase in the mean cloud∆z considered. The green line in the same figure is obtained for the whole FD without distinction between day and night or latitudinal belt. A parameterized formula

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that describes the green curve of Fig. 7 is given in Eq. (7):

τ₌a₁·∆zb₊a₂ (7)

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The aboveτ-∆z relation simply parameterizes the mean OD value for a given cloud geometrical thickness when homogeneous and optically thin (τ <2) cirrus clouds are considered. Equation 7 holds for ∆z varying from 0.5 to 5.8 km (R2₌0.984). The spread of the OD distribution around the mean for each geometrical thickness is pro-vided by Eq. (8) (R2₌0.973):

5

σ_τ₌c₁·ed1∆z₊_c

2·ed2∆z (8)

wherec₁₌0.6138,c₂₌−0.0792,d₁₌−0.9944 andd₂₌−1.5090.

In Fig. 7 the curves are superimposed to the frequency of occurrence of homoge-neous cirrus clouds as function of theτand∆z. The frequency of occurrence highlights the large number of cirrus clouds with geometrical depth between 1 and 4 km and gives

10

an idea of the distribution of cirrus clouds OD as function of geometrical thickness and vice versa.

As a conclusion, since a relation between mean BSPs and geometrical thickness exists it is plausible that also a relation (even if weaker) exists between BSP shape and OD as a consequence of theτ−∆z dependence.

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In order to verify that the shape of the BSP is mainly driven by cloud geometrical thickness and that the BSP-OD relation is only a second order effect, an analysis con-cerning the influence of OD value on the shape of the BSP must be applied to data from which the geometrical thickness dependence is removed (or at least limited). In this regard, the relation BSP-OD is investigated for cirrus clouds with nearly the same

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∆zbut varyingτ. In the upper panel of Fig. 8 the BSPs of midlatitude cirri during night-time are computed for six optical depth intervals and for fixed geometrical depths (only clouds with vertical extension from 2.1 to 2.5 km are selected so that a large number of cases is accounted for). Results show a limited variability in the shape of the BSP with changing OD value. The largest value of I_∆ found for the curves plotted in the

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the maximum (and lower values near cloud top and base). This behavior is observed for both day and night profiles and for both the climatic regions.

As a comparison with the results shown in the upper panel of Fig. 8 the lower panel shows BSPs of midlatitude cirrus clouds at nighttime computed for varying geometrical thickness (six intervals) but nearly constant optical depth (0.8–1.0, so that the number

5

of cases considered is maximized). It is demonstrated that a strong dependence be-tween the shape of the BSP and the cloud thickness exists and that the maximum of the BSP curves shifts from cloud top to cloud base with increasing cloud geometrical depth. In this case the maximumI_∆ among the curves is of 48 %. It is found that, for both latitudes and day and night, the difference indexes found when∆zis varied andτ

10

is fixed are larger (of a factor between 1.5 and 3.2) than those found for varying optical depth intervals and fixed geometrical thickness.

Results show that the cirrus cloud optical depth has a smaller but appreciable influ-ence on the shape of the BSP compared to geometrical depth.

3.5 Temperature and backscatter profile

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CALIOP Level 2 products contain temperature data derived from the GEOS-5 model and provided by the GMAO Data Assimilation System (http://gmao.gsfc.nasa.gov/ index.php) which are exploited in the investigation of the influence of temperature on the shape of the cirrus clouds BSPs. An analysis of the effect of cloud perature on BSP is performed by using the mid-layer temperature (or midpoint

tem-20

perature) of the cloud that is defined as the temperature at the geometric mid-point of the layer in the vertical dimension (http://www-calipso.larc.nasa.gov/resources/ calipso users guide/data summaries/layer/#layer top temperature).

In Fig. 3 it was shown that similar distributions of midlayer temperature characterize diurnal and nocturnal data while some differences arise when latitude is accounted for,

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extension smaller than 2 km.

In Fig. 9 the annual mean BSPs for cirrus clouds with varying midlayer temperature is shown. Only the tropical case at daytime is considered since results are very similar for both regions and times of the day. Temperature intervals of 5 K are taken into ac-count from 195 K to 245 K. Another interval comprises temperatures higher than 243 K

5

and another one is for temperatures lower than 195 K. These last two intervals contain a very limited number of clouds. Results show that mean BSPs are only weakly de-pendent on temperature. It is observed that, on average, the maximum characterizing the backscatter coefficient normalized curve increases for a decreasing in the mid-layer cloud temperature (the BSP curve becomes more peaked). Some exceptions are

any-10

way present. The effect is observed at both latitudes and at nighttime and daytime. The difference indexes (I_∆) among the BSP curves of same latitude and time of the day (ML day, ML night, tropics day and tropics night) but multiple midpoint temperatures have value that are mostly below 10 %.

The above analysis cannot highlight possible variation in the shape of the BSP as a

15

function of differences in the cloud temperature profile, but it only allows temperature to be considered as a bulk parameter.

In order to tackle possible effects of vertical temperature variations on the shape of BSP an investigation is performed which accounts for clouds with geometrical thickness between 4 and 4.5 km and analyzes separately cirri with large and small temperature

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gradients between the cloud top and bottom. For clouds with the above geometrical thickness the top and bottom temperature difference distribution is computed. Mean difference between cloud top and cloud bottom temperature is about 30 and 35 K re-spectively for ML and tropics. The cirrus clouds that fall below the first and above the third quartile of the top-bottom temperature difference distribution are compared for

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gradient is anyway very small and less than 8 % for all the situations considered. It is thus concluded that the influence of temperature on the shape of mean BSPs, both at night and day, is of minor significance if compared to the effects related with the cloud geometrical thickness.

3.6 Polynomial fitting of mean backscatter profiles

5

An analytical representation of mean BSPs measured by CALIOP is given, so that climatological shape of the BSPs of cirrus clouds in different conditions could be used by the reader.

The statistical analysis of BSPs has shown that the cloud geometrical thickness is the main parameter affecting the shape of the mean CALIOP BSP. It is found that a

10

maximum in the mean BSP is placed near the top of the cloud for small∆z (less than 2 km at daytime and 3 km at nighttime) and moves towards the cloud base with increas-ing vertical extension. Also the cloud optical depth and temperature (even weakly) af-fect the shape of the mean CALIOP-measured BSPs. The main effect of these two quantities is to modify the intensity of the maximum of backscatter (relatively to levels

15

near cloud base or top), which takes the highest values for the highest temperatures and the largest optical depths. Temperature and cloud optical depth produce second-order e_ffects on the shape of backscatter profile and thus only the influence of cloud geometrical thickness is here considered.

Since the shape of BSPs for varying∆zshows very limited dependence on latitude

20

(Figs. 5 and 6), only polynomial fittings for the day and night cases are provided. Mean BSPs obtained for the night and day cases (tropics and midlatitudes are con-sidered together) are fitted with analytical functions. The fitting function used is a two-variables (geometrical depth and height index), fifth-order polynomial:

β(∆z,h)= 4

X

j=0

∆z₊p0j p₁_j

p₁_jhj₊p₀₅h5 (9)

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where thehvariable assumes integer values from 1 to 60 and describes the vertical variation ofβfor a cloud with geometrical thickness equal to_∆z. Thus, given the cloud top altitude (z_t), the quantity derived in Eq. (9) describes a cirrus cloud normalized BS at heightz. The altitudez is simply derived from:

z₌z_t−∆z₊h−1

59 ∆z (10)

5

In Table 5 the polynomial coe_fficients for the fit of the mean BSPs of night and day cirrus clouds are given. The fit is such that in any case theI_∆ computed for the analytical and climatological mean BSP curves is less than about 6 %.

4 Application to radiative transfer computations

4.1 From mean backscatter profiles to ice-water-content profiles

10

One of the important aspects of computing mean BSPs lies in the strict relation be-tween the profile of the backscatter (and extinction) coefficient and the distribution of ice mass along the cloud vertical dimension. The IWC profile largely affects the cloud weighting function and it is thus fundamental for the derivation of the radiative fields and the computation of the energy balance of cloud layers (Maestri and Rizzi, 2003).

15

Hence, climatological information on IWC vertical distribution can potentially improve both the radiative forward models simulations of cloudy fields and inversion algorithms dedicated to the retrieval of cloud properties.

In this regard, the radiative impact of using IWC derived from the mean measured BSPs instead of vertically constant IWC is evaluated for a simple and typical case.

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models to define the distribution of the ice mass along the cloud vertical dimension and thus providing a more realistic description of the cloud structure.

The backscatter coefficient of a collection of ice crystals depends on various param-eters such as the total IWC, the particle size distribution, the particle shapes and their orientations. Information on variations of the shape and of the orientation of ice

parti-5

cles along the vertical depth of cirrus clouds is rare. Images, taken from Cloud Particle Imager, of ice particles in regions at the top, middle, and base of clouds have shown the lack of consistency in particle habits as a function of position in cirrus clouds (Law-son et al., 2006). It is thus assumed that the mixture of habits composing the PSD (i.e. the mass percentage amount of crystals in a size bin with a specific shape with respect

10

to the total mass) remains the same along the cloud height and that the crystals are either randomly oriented or horizontally oriented along the full cloud geometrical depth. Also data regarding the variation of particles’ sizes along the vertical of cirrus clouds are few and non-exhaustive (Baran, 2009). Lawson et al. (2006) show that there are only small differences in the average PSDs in the upper portions of cirrus clouds

com-15

pared to the lower portions, especially for clouds with vertical dimensions larger than 2 km. The main difference consists is a slightly more mass concentration in the lower portion, found mostly in the slightly larger tail of the lower-region average PSD.

Thus, it is similarly assumed that the shape of the PSD (i.e. the effective dimension of the ice mixture) is invariant throughout the cloud vertical extent (variations of the

20

total number of particles and IWC in the vertical are allowed). This assumption is also taken implicitly in the CALIOP retrieval algorithms to derive the extinction coefficient profile, since lidar ratio is taken constant along the cloud geometrical depth.

Currently, the largest part of numerical weather prediction or climate models parame-terize (diagnose) the cloud particle dimensions as function of prognostic variables (i.e.

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